I'm not sure how that distinction applies to that premise. — Michael

I'm not sure what the distinction is doing here at all. You introduced it. But presumably, extensionally, X is a cup if and only if X is a cup. Extensionally, we are able to substitute salva veritate. I'm not sure that works for P2. Especially with the vacillation between "seen" and "used as".

I am hunting around for something to tie down your idea.

This is the sort of argument that an anti-realist might make:

P1. A cup exists if and only if there exists some X such that X is a cup
P2. For all X, X is a cup only if X is being seen or used as a cup
C1. Therefore, a cup exists only if there exists some X such that X is being seen or used as a cup — Michael

The problem here once again is even a realist would be committed to the claim that a cup which exists out there must have the potential to be used as a cup. I don't see any difference between "being used as a cup" & "having potential for being used as a cup" , both carry the same purpose as far as they allow us to group objects under a universal like "cup"

As for "being seen", in certain forms of idealism, being "seen" it ultimately all about being within the experience of God. Now God does encounter everything apart from him as other than him, but it doesn't exist beyond his mind either. Here, the realism or irrealims distinction ironically dissappears once again.

I'm not sure what the distinction is doing here at all. You introduced it. But presumably, extensionally, X is a cup if and only if X is a cup. — Banno

According to some anti-realists, X is a cup only if it stands in a certain kind of relationship with us, just as X is a king only if it stands in a certain kind of relationship with us.

Simply saying that X is a cup if and only if X is a cup or that X is a king if and only if X is a king is vacuous, and doesn't address any philosophical dispute.

I am hunting around for something to tie down your idea. — Banno

Much like "there is no king if the monarchy is abolished" does not mean "Charles ceases to exist if the monarchy is abolished", "there is no cup if none is seen" does not mean "the extensional object ceases to exist if it is no longer seen". You seem to be pushing this latter misrepresentation, treating all anti-realisms as phenomenalism.

I don't see any difference between "being used as a cup" & "having potential for being used as a cup" , both carry the same purpose as far as they allow us to group objects under a universal like "cup" — Sirius

"So-and-so is a wife only if she has been legally married" does not mean "so-and-so is a wife only if she has the potential to be legally married".

Some might say that the mere potential to be seen or used as a cup is insufficient to be a cup; it has to actually be seen or used a cup.

Simply saying that X is a cup if and only if X is a cup or that X is a king if and only if X is a king is vacuous, and doesn't address any philosophical dispute. — Michael

That's not quite what Banno said. He said:

extensionally, X is a cup if and only if X is a cup. Extensionally, we are able to substitute salva veritate — Banno

I've bolded "extensionally" as the key term here. I think your debate is about what constitutes a cup (or a king) intensionally. Once we agree about that, picking out examples is relatively easy, but there's no vacuity involved. And no objects persist or cease to exist, depending.

If an alien species from another planet saw Moore with his raised hand, they might be just as certain as Moore that something with a specific meaning was taking place, but within their alien language game the sense of the event would be entirely different that it is for Moore. It would not be a question of doubting Moore’s assertion, but of his assertion being irrelevant to their perspective. — Joshs

In any case the alien sees a hand even if he doesn't call it such.

Cheers.

There are two distinct questions we might do well not to compound here. One is if that is a cup. The other is if that is in the dishwasher.

Extensionally, "That is a cup" will be true if and only if that satisfies "...is a cup".

Nothing here about relationships to us. So extensionally,

It does not matter how we specify the set, or how we order its elements, or indeed how many times we count its elements. All that matters are what its elements are. — Open Logic p. 25

I doubt @Michael will disagree with this. He will be aware of Fitch's Paradox, that if the only things that are true are the things that we know to be true, then we know everything.

Now my conclusion is to allow things that are true yet unknown. The cup in the dishwasher is a rough proxy for this, and Michale is right to point out that it is a it too rough. It developed from the usual antirealism hereabouts, that relies on what he has called "phenomenalism".

Again, my contention is that realism provides a better way to talk about the 'medium-size small goods" around us, but that it isn't the only way. This amounts to claiming that it is better to understand that there are true things we do not know, than to claim that we know everything.

That might provide the context for Michael's thought.

'If there is one single point which underlies the entire illusion of modern scientific materialism, it is the idea of the mind-independent object'.

'Of course there are mind-independent objects!'

'Well, name one.'

:chin:

You mention Fitch's paradox, which is also an argument against mathematical constructivism, and as you said in an earlier post, "I have however also defended a constructivist view of mathematics, an anti-realist position".

Presumably you accept that we don't know everything about maths.

And I should clarify, you talk about "all truths being known" in reference to Fitch's paradox, but the relevant claim under consideration is "all truths are knowable", a subtle but important difference.

But of course, as with your own example of maths and aesthetics, one can be an anti-realist about some things but not about others. So perhaps global anti-realism entails Fitch's paradox, but anti-realism about medium-sized dry goods (and mathematics) doesn't.

And I should clarify, you talk about "all truths being known" in reference to Fitch's paradox, but the relevant claim under consideration is "all truths are knowable", a subtle but important difference. — Michael

Not too sure about that...

(K Paradox) ∀p(p→◊Kp)⊢∀p(p→Kp). — Fitch’s Paradox of Knowability

I was mostly addressing this:

if the only things that are true are the things that we know to be true — Banno

The claim is that the only things that are true are things that can be known to be true. Fitch may attempt to prove that this entails that we know everything, but it's important to properly represent the actual claim being made by the anti-realist.

Not following that. I'll have another look tomorrow.

Not following that. — Banno

Well, let's take the SEP article:

Fitch’s paradox of knowability (aka the knowability paradox or Church-Fitch Paradox) concerns any theory committed to the thesis that all truths are knowable. Historical examples of such theories arguably include Michael Dummett’s semantic antirealism (i.e., the view that any truth is verifiable), mathematical constructivism (i.e., the view that the truth of a mathematical formula depends on the mental constructions mathematicians use to prove those formulas), Hilary Putnam’s internal realism (i.e., the view that truth is what we would believe in ideal epistemic circumstances), Charles Sanders Peirce’s pragmatic theory of truth (i.e., that truth is what we would agree to at the limit of inquiry), logical positivism (i.e., the view that meaning is giving by verification conditions), Kant’s transcendental idealism (i.e., that all knowledge is knowledge of appearances), and George Berkeley’s idealism (i.e., that to be is to be perceivable).

...

The great problem for the middle way is Fitch’s paradox. It is the proof that shows (in a normal modal logic augmented with the knowledge operator) that “all truths are knowable” entails “all truths are known”.

So the anti-realist doesn't claim that all truths are known, only that all truths are knowable. Fitch attempts to refute this by showing that this entails that all truths are known (which is taken to be an obvious falsehood), but this is an entailment that (some) anti-realists will reject.

On Fitch's paradox I think a simple solution would be to amend the knowability principle:

∀p∀q((p ⊬ (q ∧ ¬Kq)) → (p → ◊Kp))

For all p that doesn't entail that some q is an unknown truth, if p is true then p is knowable.

Which makes sense. If knowing p is a contradiction (which knowing an unknown truth is) then it’s not possible to know p, but if knowing p is not a contradiction (and if p is true) then it is possible to know p.

Yeah, but ∀p(p→◊Kp)⊢∀p(p→Kp) is valid. It's not enough for antirealists just to say they reject the entailment. Some explanation is needed.

For middle-size antirealism, if something is true then it is possible to know that it is true. This is simply a restatement of the antirealist thesis that something can be true only if it has been demonstrated. But from this it immediately follows that we know every thing there is to be known. That is,

The argument shows that if we assume p → ♢Kp then p → Kp follows. — Michael

It's not enough for antirealists just to say they reject the entailment. Some explanation is needed. — Banno

They do, e.g. by adopting intuitionist logic.

This is simply a restatement of the antirealist thesis that something can be true only if it has been demonstrated. — Banno

That's not the antirealist thesis. The antirealist thesis is that something is true only if it can be demonstrated. You are, again, treating the critic's conclusion as the proponent's claim.

But as a question to you, do you believe that all mathematical truths are known? You claimed in an earlier post that you are a mathematical antirealist.

That's not the antirealist thesis. The antirealist thesis is that something is true only if it can be demonstrated. You are, again, treating the critic's conclusion as the proponent's claim. — Michael

Ok. This is simply a restatement of the antirealist thesis that something can be true only if it can be demonstrated. Hence, if something can be true then it is possible to know that it is true. Hence, the antirealist knows everything that is true.

Hence, if something can be true then it is possible to know that it is true. Hence, the antirealist knows everything that is true. — Banno

And as mentioned before, the antirealist rejects the conclusion. They might claim that every truth is knowable but that some truths are unknown.

Fine.

And as mentioned before, the antirealist rejects the conclusion. They might claim that every truth is knowable but that some truths are unknown. — Michael

How can the anti-realist justify the claim that all unknown truths are knowable? You would have to know them to know they are knowable, no?

what I said.

How can the anti-realist justify the claim that all unknown truths are knowable? You would have to know them to know they are knowable, no? — Janus

How can the realist justify the claim that some unknown truths are unknowable? You would have to know them to know they are unknowable, no?

As I see it, nearly all these debates are implicitly centred around the correspondence theory of truth, the way in which propositions do or do not correspond with actual states of affairs in the world. I think the poorly-named 'antirealist' attitude is nearer to constructivist theories of truth, that our judgements of what is the case are constructed on the basis of the combination of sensory and rational judgement. In other words, it calls into question the criterion of 'mind-independence', but not on the same grounds that correspondence theory appeals to it. It does so on the basis of another perspective. From this perspective, experience is not a direct reflection of an external reality, but rather constructed through processes of cognition, cultural context, and sensory experience. This view questions mind-independence by suggesting that what we take to be true is deeply conditioned by the structure of our conceptual frameworks and the limitations and particularities of perception.

While correspondence theory appeals to a straightforward, objective standard for evaluating truth (like Banno's kitchen utensils), constructivist or coherence theories call attention to the interpretative acts that shape judgment. This doesn't mean that anti-realists deny the existence or even the reality of an external world; rather, that the truth-value of our propositions depends on how we organize, interpret, and construct our experiences of it. So what it calls into question is the chimeric notion of 'mind-indepedence' (which is what Banno appeals to with respect of all the cups he cannot see).

But to offer a more substantive response, one of these is true:

1. "all truths are knowable" is true and knowable
2. "some truths are unknowable" is true and knowable
3. "some truths are unknowable" is true and unknowable

If knowledge is justified true belief then one of these is true:

4. "all truths are justifiable" is true and justifiable
5. "some truths are unjustifiable" is true and justifiable
6. "some truths are unjustifiable" is true and unjustifiable

The interesting thing about (6) is that if it's true then realism is both true and unjustifiable. Technically that's consistent with realism, but perhaps not of much comfort to the realist who seeks to justify his position.

So pragmatically that leaves us with (4) and (5). How do we decide between them without knowing any unknown truths?